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Ultracold atoms, molecules, and ions: Optical Lattice Emulators and beyond

Explore the new era in cold atom research, focusing on systems with strong interactions. Resolve long-standing questions in condensed matter physics and gain new perspectives on strongly correlated systems. Discover new phenomena in quantum many-body systems of ultracold atoms.

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Ultracold atoms, molecules, and ions: Optical Lattice Emulators and beyond

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  1. Ultracold atoms, molecules, and ions: Optical Lattice Emulators and beyond Eugene Demler Harvard University E. Altman (Weizmann), E. Dalla Torre (Weizmann), A. Imambekov (Yale), T. Giamarchi (Geneva), T. Kitagawa (Harvard),S. Pielawa (Harvard)

  2. Strongly correlated systems of cold atoms • Optical lattices • Feshbach resonances • Low dimensional systems • Systems with long range interactions • (Coulomb interaction for trapped ions, • dipolar interactions for polar molecules)

  3. New Era in Cold Atoms Research Focus on Systems with Strong Interactions Goals • Resolve long standing questions in condensed matter physics • (e.g. origin of high temperature superconductivity) • Resolve matter of principle questions • (e.g. existence of spin liquids in two and three dimensions) • New perspective on strongly correlated systems: • e.g. higher order correlation functions revealed in noise • New phenomena in many-body systems • e.g. coherent far from equilibrium dynamics

  4. New Phenomena in quantum many-body systems of ultracold atoms Complementary detection schemes- Single shot vs steady state measurements Long intrinsic time scales- Interaction energy and bandwidth ~ 1kHz- System parameters can be changed over this time scale Decoupling from external environment- Long coherence times Can achieve highly non equilibrium quantum many-body states

  5. Higher order correlations revealed in noise Fluctuations in low dimensional systems Atom-chip experiments Interference between independent condensates Correlations encoded into fringe statistics Hofferberth et. al. Nature Phys. 2008 (Vienna group)

  6. v Nonequilibrium dynamics of Hubbard model Instability of a moving condensate in an optical lattice Theory: Altman et al. PRL 2005 Experiment: Mun et al. PRL 2007 also Fertig et al. PRL 2004 McKay et al. Nature 2008 Dynamical instability in 3d lattice, Smearing of instability in 1d lattice,

  7. Quantum noise as a probe of non-equilibrium dynamics Ramsey interferometry and many-body decoherence

  8. Ramsey fringe visibility time Dynamics in 1d: Ramsey interference Interaction induced collapse of Ramsey fringes. Spin echo • Experiments in 1d tubes: • Widera et al. • PRL (2008)

  9. Interaction induced collapse of Ramsey fringesin one dimensional systems How to distinguish decoherence due to many-body dynamics? Luttinger liquid approach Evolution of spin distribution functions Only q=0 mode shows complete spin echo Finite q modes continue decay The net visibility is a result of competition between q=0 and other modes

  10. NEW PERSPECTIVE ON MANY-BODY SYSTEMS QUANTUM MANY-BODY SYSTEMS IN THE PRESENSE OF NONEQUILIBRIUM NOISE

  11. Question: Trapped ions Ultracold polar molecules E What happens to low dimensional quantum systems when they are subjected to external non-equilibrium noise? One dimensional Luttinger state can evolve into a new critical state. This new state has intriguing interplay of quantum critical and external noise driven fluctuations

  12. A brief review:Universal long-wavelength theory of 1D systems Haldane (81) Displacement field: Long wavelength density fluctuations (phonons): Weak interactions: K >>1Hard core bosons: K = 1Strong long range interactions: K < 1

  13. 1D review cont’d: Wigner crystal correlations Wigner crystal order parameter: No crystalline order ! Scale invariant critical state (Luttinger liquid)

  14. 1D review cont’d:Effect of a weak commensurate lattice potential How does the lattice potential change under rescaling ? Quantum phase transition: K<2 – Pinning by the lattice (“Mott insulator”) K>2 – Critical phase (Luttinger liquid)

  15. + + + + + + + + + + - - - - - - - - - - New systems more prone to external disturbance Ultracold polar molecules E Trapped ions (from NIST group )

  16. Linear ion trap Linear coupling to the noise:

  17. Measured noise spectrum in ion trap From dependence of heating rate on trap frequency. f Monroe group, PRL (06), Chuang group, PRL (08) • Direct evidence that noise spectrum is 1/f • Short range spatial correlations (~ distance from electrodes)

  18. + + + + + + + + + + - - - - - - - - - - Ultra cold polar molecules E Polarizing electric field: Molecule polarizability System is subject to electric field noise from the electrodes !

  19. + + + + + + + + + + - - - - - - - - - - Long wavelength description of noisy low D systems

  20. + + + + + + + + + + - - - - - - - - - - Component of noise at wavelengths near the inter-particle spacing Long wavelength component of noise Effective coupling to external noise >> The “backscattering” z can be neglected if the distance to the noisy electrode is much larger than the inter-particle spacing.

  21. + + + + + + + + + + - - - - - - - - - - Effective harmonic theory of the noisy system (Quantum) Langevin dynamics: Thermal bath External noise Dissipative coupling to bath needed to ensure steady state (removes the energy pumped in by the external noise) Implementation of bath: continuous cooling

  22. Wigner crystal correlations Case of local 1/f noise: • Decay of crystal correlations remains power-law. • Decay exponent tuned by the 1/f noise power. 1/f noise is a marginal perturbation ! Critical steady state

  23. + + + + + + + + + + - - - - - - - - - - Kc Critical state 2 Localized F0 /h Effect of a weak commensurate lattice potential Without lattice: Scale invariant steady state. How does the lattice change under a scale transformation? Phase transition tuned by noise power (Supported also by a full RG analysis within the Keldysh formalism)

  24. + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Kc 2D superfluid 1D critical 1/4 F0 /h 1D-2D transition of coupled tubes Scaling of the inter-tube hopping:

  25. Kc 2D superfluid 2 1D critical 2D crystal F0 /h Global phase diagram Inter-tube tunneling Inter-tube interactions Kc Kc Critical state 1 2D superfluid 1D critical 2D crystal 1/4 F0 /h F0 /h Both perturbations

  26. SummaryNew perspective on physics of strong correlationsfrom systems of ultracold atoms, molecules, ions • Nonequilibrium dynamics • Analysis of higher order correlation functions Example: Decay of Ramsey fringes in one dimensional systems • Effects of external noise on quantum critical states • new critical state • new phases and phase transitions tuned by noise Can be studied with ions and ultracold polar molecules

  27. Trapped ions Ultracold polar molecules 2D superfluid 1D critical E 2D crystal Kc 2 F0 /h New critical state of 1d systems subject to 1/f noise • Decay of crystal correlations remains power-law. • Decay exponent tuned by the 1/f noise power. Novel phase transitions tuned by acompetition of noise and quantum fluctuations

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